Science Forums 2

[Jay-qu]

Originally Posted by Ben

Missing an hbar on the LHS? Not important. But I am slightly troubled by the absence of a potential term in your Hamiltonian. Is this to do with the qualification "in free space"?
Yeah, I have something similar here, but without in the exponent. Is this strictly required? And why have you vectorized the spatial component x? (if that's what it is)
OK, so I got, as then, after a bit of manipulation, using God's units, and ditching the in the exponent

Yes, take free space to mean in the absence of a potential.

I must apologise for the few mistakes I have made, firstly I have not really been consistent with my factors or hbar and e.

Having the x as a vector simply saves me writing f(x,y,z) everywhere.

Um. I got a mass term in there - Do I need to worry about that?

Also, I think I may have an argument that says that your `vector potential' is actually a connection 1-form on the bundle. Leave it with me a while.

Hmm Im not sure about the mass term.. I think I have made a mistake above and the mass term should not appear in the gauge transformation - as it will not be an invariant with it there..